The lawsuits, filed in states with key races, mark the tail-end of a months-long legal push by Democrats and Republicans to define the rules for voting in Tuesday's election.
Cobb County has been overnighting ballots to affected voters and estimated on Monday that 276 voters had yet to receive a ballot.
Lawyers aligned with both Democrats and Republicans have brought waves of lawsuits over the rules for the upcoming election.
Judge Casey McGinley in Arizona, who blocked the Conchise County hand count on Monday, said he was presented "no evidence" that the machine tabulation of ballots is inaccurate.
Another hand count in Nevada’s rural Nye County was shut down in favor of machine counting after the state supreme court struck down parts of the process.